The angular velocity is 16.2 rev/min
Step-by-step explanation:
The relationship between angular velocity and linear speed for a body in circular motion is given by the equation
[tex]v=\omega r[/tex]
where
v is the linear speed
[tex]\omega[/tex] is the angular velocity
r is the radius of the circle
For the hamster in this problem, we have:
v = 17 cm/s = 0.17 m/s is the linear speed
r = 10 cm = 0.10 m is the radius of the wheel
Solving the equation for [tex]\omega[/tex], we find the angular velocity:
[tex]\omega=\frac{v}{r}=\frac{0.17}{0.10}=1.7 rad/s[/tex]
And keeping in mind that:
[tex]1 rev = 2 \pi rad\\1 min = 60 s[/tex]
We can convert into revolutions per minute:
[tex]\omega = 1.7 rad/s \cdot \frac{60 s/min}{2\pi rad/rev}=16.2 rpm[/tex]
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The wheel spin with angular velocity of 16.2 revolution per minute.
The linear velocity is given as,
[tex]v=rw[/tex]
Where r is radius and w is angular velocity.
Given that, [tex]v=17cm/s,r=10cm[/tex]
Substitute, [tex]w=\frac{v}{r}=\frac{17}{10} =1.7rad/s[/tex]
We know that,
[tex]1rev.=2\pi radian[/tex]
[tex]1min=60 seconds[/tex]
So that,
[tex]w=\frac{1.7*60}{2\pi} =16.2rev./min[/tex]
Hence, the wheel spin with angular velocity of 16.2 revolution per minute.
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